Identity Morphism

The morphism mapping Object a Category to itself

• Every object has a identity morphism

Consider the identity of category $X$

$$\begin{array}{c}{\text{id}}_X:X\to X\\ f\circ {\text{id}}_X=f={\text{id}}_X\circ f\end{array}$$

• Depending on the context, the subscript may not be neccessary

Identity Composition

Composing with the identity has no effect.